Usage

Arguments

The id of the source vertex, for edge_connectivity it
can be NULL, see details below.

target

The id of the target vertex, for edge_connectivity it
can be NULL, see details below.

checks

Logical constant. Whether to check that the graph is connected
and also the degree of the vertices. If the graph is not (strongly)
connected then the connectivity is obviously zero. Otherwise if the minimum
degree is one then the edge connectivity is also one. It is a good idea to
perform these checks, as they can be done quickly compared to the
connectivity calculation itself. They were suggested by Peter McMahan,
thanks Peter.

Details

The edge connectivity of a pair of vertices (source and
target) is the minimum number of edges needed to remove to eliminate
all (directed) paths from source to target.
edge_connectivity calculates this quantity if both the source
and target arguments are given (and not NULL).

The edge connectivity of a graph is the minimum of the edge connectivity of
every (ordered) pair of vertices in the graph. edge_connectivity
calculates this quantity if neither the source nor the target
arguments are given (ie. they are both NULL).

A set of edge disjoint paths between two vertices is a set of paths between
them containing no common edges. The maximum number of edge disjoint paths
between two vertices is the same as their edge connectivity.

The adhesion of a graph is the minimum number of edges needed to remove to
obtain a graph which is not strongly connected. This is the same as the edge
connectivity of the graph.

The three functions documented on this page calculate similar properties,
more precisely the most general is edge_connectivity, the others are
included only for having more descriptive function names.

Value

A scalar real value.

References

Douglas R. White and Frank Harary: The cohesiveness of blocks in
social networks: node connectivity and conditional density, TODO: citation